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zavuch27 [327]
3 years ago
5

a contract is good in the base of a circular fountain on the blueprint the base of the food has a date diameter of 18 cm the boo

k has the skill address it to me and so forth see what will be the actual area of the base of the fountain and the squares the fda is blue to the nearest 10th of a square foot
Mathematics
1 answer:
lozanna [386]3 years ago
4 0

Answer:  452.4\ ft^2

Step-by-step explanation:

<h3> The complete exercise is "A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 18 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot."</h3>

The following formula can be used for calculate the area of a circle:

A=\pi r^2

Where "r" is the radius of the circle.

Let be "x" the actual diameter in feet of the base of the fountain.

You know that the  blueprint has a scale of  3\ cm:4\ ft, then, you can set up the following proportion:

\frac{4}{3}=\frac{x}{18}

Solving for "x", you get:

(18)(\frac{4}{3})=x\\\\x=24

Since the radius of a circle is half its diameter, you know that the actual radius  of  the base of the fountain is:

r=\frac{24\ ft}{2}=12\ ft

Now you can substitute the radius into the formula in order to calculate the actual area of the base of the fountain. Rounded to the nearest 10th, this is:

 A=\pi (12\ ft)^2=452.4\ ft^2

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The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If
attashe74 [19]

Answer:

t=7.85 years

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

\frac{dP}{dt}=aP

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\frac{dP}{P}=adt

Integrating each side of the equation.

\int \frac{dP}{P}=\int adt

ln(P)=at+c

P=e^{at+c}

P=e^{c}e^{at}=Ce^{at}

To find C we need to use the initial condiction, it means evaluae P at t=0.

P_{0}=Ce^{0}=C

P=P_{0}e^{at}

Now, we use the sentence  the population has doubled in 5 years.

2P_{0}=P_{0}e^{a5}

We can find "a" in this condition.

2=e^{a5}

ln(2)=a5

a=\frac{ln(2)}{5}

a=0.14

Finally, let's find how long will it take to triple.

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I hope it helps you!

4 0
2 years ago
Help!! <br><br> I think I got these wrong, so please help!! Thank you!
Andrew [12]

Answer:

(x+3)(x+4)(x-4)

x+2 and x-3 are not factors but x-4 is

Step-by-step explanation:

let's factor it :)

x^3 + 3x^2 - 16x -48

first we will factor this:

x^3 + 3x^2

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then factor the second part :

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so now,

x^2(x + 3) - 16(x + 3)

factor out x+3

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factor x^2 - 16

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Answer:

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kakasveta [241]
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